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The algebra of Boolean matrices, correspondence functors, and simplicity (1902.05422v1)
Published 13 Feb 2019 in math.RT, math.CO, math.CT, math.GR, and math.RA
Abstract: We determine the dimension of every simple module for the algebra of the monoid of all relations on a finite set (i.e. Boolean matrices). This is in fact the same question as the determination of the dimension of every evaluation of a simple correspondence functor. The method uses the theory of such functors developed in [BT2, BT3], as well as some new ingredients in the theory of finite lattices.
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